The proposed budget is about $50 million less than the amount sought a year ago, but about $1 billion more than the agency's current spending plan. Billions of dollars would be set aside to continue operations on the International Space Station, keep up the work on interplanetary missions, expand the nation's network of Earth-observing satellites and upgrade aerospace technologies. However, the headline-grabber in the budget is the asteroid retrieval mission, which is budgeted for $105 million in spending during the fiscal year beginning in September.

"This mission represents an unprecedented technological feat that will lead to new scientific discoveries and technological capabilities and help protect our home planet," NASA Administrator Charles Bolden said in a statement accompanying the budget request.

Planning documents suggest that the space agency would launch a probe powered by a next-generation solar electric propulsion system sometime around 2017, to rendezvous with a 7- to 10-meter-wide (25- to 33-foot-wide) asteroid around 2019. A collapsible shroud would be wrapped around the asteroid, and then the probe would pull the space rock to a stable point in high lunar orbit or at a gravitational balance point beyond the far side of the moon.

Speaking on condition of anonymity, officials familiar with the plan told NBC News that NASA was already beginning the work to identify a candidate asteroid. The 2014 budget includes $78 million for planning the mission, and $27 million to accelerate NASA's efforts to detect and characterize potentially hazardous asteroids. NASA's chief financial officer, Elizabeth Robinson, indicated that this spending would come in addition to the $20 million that the space agency currently spends annually on asteroid detection.

The plan for the mission was formally unveiled less than two months after an asteroid streaked through the atmosphere and broke up over Russia. The breakup sparked a meteor blast that shattered windows and injured more than 1,000 people.

That asteroid was thought to have been about 17 meters (55 feet) wide. The type of asteroid targeted for the future NASA mission, in contrast, would be too small to pose a threat to Earth — even if it were to break loose somehow and plunge through the atmosphere.

Astronauts to visitBolden said the asteroid-grabbing mission meshed with NASA's plans to head off cosmic threats as well as to prepare for deep-space human exploration. Eventually, astronauts would be sent to study the captured asteroid and bring back samples, most likely during a beyond-the-moon test mission that's already planned for 2021.

"This asteroid initiative brings together the best of NASA's science, technology and human exploration efforts to achieve the president's goal of sending humans to an asteroid by 2025," Bolden said. "We will use existing capabilities such as the Orion crew capsule and Space Launch System rocket, and develop new technologies like solar electric propulsion and laser communications — all critical components of deep-space exploration."

A senior administration official told NBC News on condition of anonymity that the added cost of the asteroid mission would be around $1 billion, spread over several years. That figure doesn't include the estimated $35 billion that is being paid out to develop the SLS/Orion system for deep-space human flights.

As Bolden noted, the asteroid mission would satisfy President Barack Obama's space exploration goal for 2025, and allow NASA to turn its attention to sending astronauts to Mars and its moons in the 2030s. Last week, Bolden signaled that other potential objectives, such as sending humans back to the moon, were not on the agenda for the foreseeable future.

Nevertheless, some lawmakers want NASA to go in a different direction: A bipartisan group of House members last week reintroduced a bill calling on the space agency to develop a plan for establishing a permanent human presence on the moon.

"Last year, the National Research Council committee charged with reviewing NASA’s strategic direction found that there was no support within NASA or from our international partners for the administration’s proposed asteroid mission," Rep. Frank Wolf, R-Va., said in a statement. "However, there is broad support for NASA to lead a return to the moon. So the U.S. can either lead that effort, or another country will step up and lead that effort in our absence — which would be very unfortunate."

No guaranteesNASA's $17.7 billion spending plan accounts for less than half a percent of Obama's $3.8 trillion request to Congress for fiscal 2014. The entire budget is likely to come under close scrutiny in the Republican-controlled House as well as the Democratic-controlled Senate, and there's no guarantee that the final version will look anything like the White House's proposal. In fact, last year's budget request ended up going nowhere. Instead, the federal government is currently operating under a budget sequestration plan that cut back on previous spending levels.

"This was a meat-ax approach that I think nobody initially intended to have take effect," White House science adviser John Holdren said Wednesday during a budget briefing.

Holdren said the total amount of money budgeted for research and development in 2014 would come to $142.8 billion, which represents a "small decline" in inflation-adjusted dollars compared with 2012 spending levels.

"Although this is not the budget that we would want if financial times were better, it reflects an extraordinary effort by this administration to preserve a key investment in research, development, innovation and STEM [science, technology, engineering and math] education that our country's future requires," Holdren said.

Update for 9:15 p.m. ET April 10: NASA's asteroid retrieval mission could complement commercial efforts to identify and exploit bigger near-Earth objects, said Chris Lewicki, president of the Planetary Resources asteroid-mining venture. He said he's already been involved in an "ongoing discussion" about how such a mission could benefit the public as well as private enterprise.

"Maybe this is a model for a COTS-like program where there are operations put in place for private industry to help develop a marketplace," Lewicki told NBC News.

But Lewicki said the mission will not be easy. "It represents something new that will require NASA and the contractors that help them do it to really stretch their capabilities," he said.

For example, Lewicki said it would be "very challenging" to identify and track deep-space objects in the size range that NASA is targeting — that is, 7 to 10 meters wide. Such objects usually can't be spotted unless they make a close approach to Earth.

"With what's been proposed in the budget, NASA is putting more money on the table to accelerate and leverage more observation activities," Lewicki said. "The question is, is that enough? And is it going to be soon enough?"

Correction: I originally wrote that the full budget proposal was seeking $3.8 billion, but it's actually $3.8 trillion. Unfortunately, it's not the first time one of those wayward "illions" has slipped through the net. Thank goodness I have sharp-eyed commenters to set me straight.